An Extended Lindley Distribution with Application to Lifetime Data with Bayesian Estimation - Alizadeh, Morad; Ranjbar, Vahid; Eftekharian, Abbas; Kharazmi, Omid (Statistics, Optimization & Information Computing, 2021)
A four-parameter extended of Lindley distribution with application to lifetime data is introduced. It is called extended Marshal-Olkin generalized Lindley distribution. Some mathematical properties such as moments, skewness, kurtosis and extreme value are derived. These properties with plots of density and hazard functions are shown the high flexibility of the mentioned distribution. The maximum likelihood estimations of proposed distribution parameters with asymptotic properties of these estimations are examined. A simulation study to investigate the performance of maximum likelihood estimations is presented. Moreover, the performance and flexibility of the new distribution are investigated by comparing with several generalizations of Lindley distribution through two real data sets. Finally, Bayesian analysis and efficiency of Gibbs sampling are provided based on the two real data sets.